Haptic Rendering of Biological Elastic Propertiesbased on Biomechanical Characterization

Mehdi Boukallel, Maxime Girot and Stephane RegnierLaboratoire de Robotique de Paris

Universite Pierre et Marie Curie - Paris 6CNRS - FRE 2507

18, route du Panorama - BP 6192265 Fontenay-aux-Roses Cedex, Franceboukallel, girot, regnier@robot.jussieu.fr

Abstract— This paper deals with the design of a micro-forcesensing device for biomechanical characterization of biologicalsamples. This device combines (SPM) techniques and advancedrobotics approaches and allows to carry out in vitro prolongedobservations as well as biomechanical characterization experi-ments. Elastic properties of biological samples are reflected tothe macroscale during the mechanical characterization processby means of a haptic sensing device. Non-linear elasticity theoryformalism is used in order to achieve realistic elastic rendering.Mechanical characterization experiments are conducted on hu-man tumoral Epithilial Hella cells in order to demonstrate theefficiency and viability of the proposed system.

I. INTRODUCTION

It is now well established that variety of cells aresensitive to mechanical disturbances from their environment.The response of cells to mechanical inputs is critical ingoverning cell behavior, not only in cell culture, but alsoin extension to the physiology of whole organisms as well.This process by which cells convert mechanical stimuliinto biochemical signals is called mechanotransduction.Because cells are mechanically coupled to their environment,changes in the extracellular matrix (ECM) or cell mechanicscan dramatically change the cell behavior. For example,hepatocytes, mammary epithelial cells, capillary endothelialcells and fibroblasts in culture can be switched from a growthstate to a differentiated, non-proliferating state by modifyingthe stiffness or adhesivity of the ECM. Because of the strongin vitro and in vivo evidence that cell mechanics governscell behavior, it is not surprising that many different humandiseases may arise from abnormalities in the mechanicalenvironment surrounding cells or the ability of cells toproperly respond to these forces. For example it is welladopted that tumors are stiffer than normal tissue, as theyare frequently detected through physical palpation. In cancermetastasis, tumor cells must dramatically change theirphysical interactions with surrounding cells and ECM inorder to break away, begin migrating, invade blood vessels,extravasate, and grow at distant sites [1]- [3]. This is oneof many examples on how cells in a pathological state stopto obey normal biophysical rules, with serious detrimentalconsequences.The treatments of many diseases depend in part upon

targeting mechanical processes. Understanding cellsmechanotransduction will not only provide a more completeunderstanding of cell behavior, but will also establish newopportunities for increasing the overall efficiency of treatmentof pathologies which have a basis in physical perturbations.Thus, the ability to study accurately both mechanical responseand their inferences on individual cells is a key componentin understanding the complex biological behavior in theirenvironment (growth, development, auto-repair, ...).

Up to date, several robotics and microrobotics experimentalsetups have been developed to identify the control mechanismsof both individual cell and tissues mechanical responses [4]-[10]. Among these systems, the most promising ones involvesScanning Probe Microscopy (SPM) techniques for nanoscale.The significant research involving AFM make possible themeasuring of relevant cells mechanical properties (Young’smodulus, bulk modulus, surface roughness, cell adhesion,...) at the microscale or to investigate cell adhesion andmolecules involved in receptor-ligand interactions at thenanoscale [11]- [15]. However, most of these studies have notbeen performed in biological clean room environment. Sinceelementary biological functions and mechanical propertiesof biological cells are widely affected by the experimentalconditions, identified properties and behaviors may not berelevant. As the reaction of the biological samples to stressvary greatly in a given lapse time, it is important to monitorthe cell response continuously in an in vitro environment.Mechanotransduction studies based on AFM techniques arecommonly carried out by standard commercial cantileverswith a sharp tip. Some problems can be associated with theuse of sharp cantilevers. The nanometers size dimensions oftips can cause important local strains which are higher thanelastic domain. Furthermore, depending of the magnitudeof the applied force on the soft samples, cantilevers tipsas well as the samples can be easily damaged so that thelocal strain applied in the indented area changes. Since softorganic tissues exhibit very complex mechanical behavior(non-linear, anisotropic, viscoelastic and in some cases alsoviscoplastic behavior), approaches based on soft contactmechanics are more suitable. This issue has been addressed

1-4244-0259-X/06/$20.00 ©2006 IEEE

in our previous work by using a tipless chemically inertcantilever which is less prone to sharp tip problems [16].Finally, studies involving AFM techniques for biomedicalapplications are mainly focused on the accurate determinationof the cell mechanical response. Seldom are the studieson mechanotransduction which are extended to in vitrotactile sensing of the cell response. Tactile sensing can be apromising solution when combined to traditional biochemicalapproach to investigate the complex mechanical behaviorof cells in their environment and the mechanisms by whichbiochemical signals are transmitted. Reflect forces as well asphysiological changes of cells to the macroscale can lead toa better understanding of the mechanotransduction process.This issue has been addressed in this paper by the developedForce Sensing Bio-Microscope (FSBM) system. This devicecombines SPM techniques and advanced robotics approachesallowing to carry out in vitro prolonged observations onbiological samples. A haptic sensing device with 1 DOFis used for investigate either elasticity, elasticity hysteresisor viscoelasticity behaviors. Mechanical characterizationexperiments are conducted on human tumoral Epithilial Hellacells in order to demonstrate the efficiency and viability ofthe proposed system.

In the next section, the experimental device produced toperform cell mechanical characterization based on sensingfeatures is presented and detailed in the section II. SectionIII is devoted to the description of the mechanical modelingof the haptic device. Section IV presents the description ofour preliminary experimentation and analysis of cells mechan-ical characterization using the Force Sensing Bio-Microscope(FSBM) under in vitro conditions on human tumoral adherentcervix Epithelial Hela cells.

II. EXPERIMENTAL SETUP OVERVIEW

The FSBM experimental setup provides suitable conditionsfor study in controlled environment so that the biological cellscan be kept several hours in living state by using a cageincubator. Moreover, the mechanical measurement process canbe done on the biological sample on an extended lapse of time.Figure 1 shows the overview of the developed FSBM device.The FSBM is composed mainly with four units: the mechanicalsensing unit which performs detection, positioning and sensingfeatures, the imaging/grabbing unit for imaging features, theclean room in vitro unit which allows experiments to beconducted in biological environment and the haptic devicefor the realistic sensing of biological elastic properties. Twocomputers (master and slave) are used to control the units.The slave computer is assigned to control the mechanicalsensing, the imaging and the clean room units while themaster computer is dedicated for the haptic device. Theslave computer is connected to the master computer usinga UDP communication. A user definable interface based onMATLAB R© communication toolbox is developed to allowsefficient flow communication. The bilateral configuration of

the connection between the master and the slave computers ispresented in figure 2.

Cage incubator

CCD camera

Inverted mic roscope

3 DOF Microposit ioning

s tage

Anti-vib ration tab le

50 mm

Fig. 1. The FSBM experimental setup overview.

A. Mechanical sensing unit

The FSBM mechanical sensing unit is based on the detectionof the deflection of a cantilever by an optical technique. Afour quadrant photodiode with internal amplifiers associatedto a low power collimated laser diode (wavelength 650nm) are used in order to perform both axial and lateralnanoNewtons forces measurements. The total sensing area ofthe photodiode is 7 mm2 with a spectral response from 400to 1100 nm. The optical path of the Gaussian laser beam isoptimized using a pair of mirrors and a aspheric condenserglass lens. Hence, a sensitive and accurate detection deviceis produced for the aim of our study. The sensitivity of theoptical detection device is 5 mV /µm.

A low spring constant (0.2 N/m) uncoated tiplesssilicon cantilevers is used as probe for the cell mechanicalcharacterization. The lever is 450 µm long, 90 µm large and2 µm thick. The sample to be studied is accurately positionedbelow the cantilever by a 3 DOF’s (x,y and z) micropositioningencoded stage with a submicrometer resolution (0.1 µm). Thekinematic features of the micropositioning stage allows toachieve accurate mechanical measurements in a workspace of25 x 25 x 25 mm3 with good repeatability. The configuration

Master PCRT Linux

FSBM Device

Mechanical

Data acquisi t ion

board

Video acquisitionboard

Ser ia l port communication

Slave PC Windows

UDP communicat ion

Clean room unit

Imaging uni t

Haptic device

User/supervisor

Sensing unit

Fig. 2. Block diagram of the FSBM device.

of the mechanical sensing unit, including the optical detectiondevice, is presented in figure 3. A magnified picture of thecantilever with the focused laser beam on its reflective surfaceis shown in the same figure.

Fig. 3. The mechanical sensing unit.

B. Imaging/grabbing unit

The FSBM imaging/grabbing unit consists of an invertedmicroscope (Olympus IMT-2) with Nikon 10x and 20x objec-tives. A phase contrast device is mounted on the microscopefor precise contrast operation. The inverted microscope isfitted out with a CCD camera (754x488 pixels resolution).Using a frame grabber and a specialized imaging PCI (MatroxImaging) device associated to the CCD camera, automaticmechanical characterization based on image features trackingis achieved.

C. Clean room in vitro unit

The biological samples need specific requirements to bekept alive outside the vivo conditions to carry out prolongedobservations. Besides the biological nutrition medium, biolog-ical cells need 37 oC in temperature and 5% of CO2 gas.The FSBM is equiped with a controlled heating module whichmaintains temperature on the cage incubator at 37 oC using asingle thermocouple. The cage incubator ensures a temperaturestability within the 0.1 oC. A mixed stream composed by a5% CO2 and humidified air is fed into a small incubatingchamber containing the biological samples, avoiding in thisway condensation on the cage walls that could damage themechanical parts of the microscope and the micropositioningstages. The whole system including the FSBM is placedin a negative pressure clean room to protect the biologicalenvironment.

D. Haptic device

The haptic device consists of Maxon R© DC motor coupledwith an accurate encoder. The device performs two functions: accurate placement of the cantilever above the sample (zdirection) and elastic and visco-elstic haptic rendering. Theoutstanding technical features of the the DC motor and the

TABLE IHAPTIC DEVICE PARAMETER DATA

Parameter Numerical valueMaximum current input 2.15 A

Nominal voltage 40 Volts

Inductance resistance 2 OhmsMaximum torque Γm 0.11 Nm

Maximum speed 8200 tr/mnAngular range infinite

Angular resolution 1/5000 trEfficiency 86 %

Radius of the Aluminum disc 35 mmMaximum tangential force 2.86 N

components working with allow effective haptic renderingat the macroscale. Besides their compact design, the devicepresents linear behavior between both the voltage/speed andthe load/speed. Since no magnetic detent is used for themotor fabrication, electromagnetic interferences are reduced.Furthermore, the haptic device is able to bear high overloadwhich increase its robustness to bad manipulation. Figure 4presents the overview of the haptic device. A low mass inertiaAluminum ergonomic disc are fixed to the motor spindle inorder to perform efficient manipulation and sensing tasks.The table I summarizes the relevant technical features of theDC motor and the encoder.

Encoder

DC motor

Aluminiumdisc

Fig. 4. The haptic device.

III. MECHANICAL MODELING AND CALIBRATION OF THESENSING DEVICE

In order to perform accurate sensing tasks at the microscale,we have conducted experiment for modeling the mechanicalbehavior of the haptic device.

A. Mechanical behavior

The angular position θ and the speed Ω as a functionof the input current I are presented in figure 5(A) and (B)respectively. These curves emphasize the role of the load indecreasing the efficiency of the haptic device but reveal a goodlinear behavior between speed and current.

Figure 6 shows the load influence on the speed/torquediagram. The torque/speed experimental data are fitted with

0 0.5 10

5

10

15

Current I (A)

An

gu

lar

Po

siti

on

θ (

rd)

0 0.5 10

5

10

15

20

25

30

35

Current I (A)

Sp

eed

Ω (

rd/s

)

(A) (B)

Load

Unload

Load

Unload

Fig. 5. (A) Angular position θ as a function of the current I . (B) Speed Ωas a function of the current I .

linear interpolation function. The slope of the unload curveis in a good agreement with the manufacturer specifications(Torque constant). The torque Γm of the haptic deviceis measured using a calibrated force cell. One can seethat speed decrease linearly with increasing torque for thetwo cases. Based on this diagram, the identification ofthe load torque/speed constant is achieved by calculatingthe slope of the load curve (Ktorque/speed = 6.2 mN.rd−1.s).

0 5 10 15 20 250

0.01

0.02

0.03

0.04

0.05

0.06

Speed Ω (rd/s)

To

rqu

e Γ

m (

Nm

)

Load

Unload

Fig. 6. Influence of the load for the torque/speed behavior.

Figure 7 presents experimental results of hysteresis iden-tification. For this purpose, the encoder output is monitoredfor an increasing and decreasing values of the input current Iduring 2 cycles. The sensing device exhibits a weak hysteresiswhatever the rotation direction (clockwise and anti-clockwise).

B. Time and frequential response

The haptic device is modeled as a SISO (Single Input,Single Output) system with current I applied to the statoras the input and the speed Ω of the rotor as the output. Sincethe current-speed obey to linear relationship (cf. figure 7), theresulting model can be considered as an LTI (Linear TimeInvariant) system. The step response of the SISO model ispresented in figure 8. The time response is fitted with a secondorder H(s) system as

0.4 0.2 0 0.2 0.4 0.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Current I (A)

An

gu

lar

po

siti

on

θ

(rd

)

Cycle 1 Clockwise

Cycle 2 Clockwise

Cycle 1 Anticlockwise

Cycle 2 Anticlockwise

Fig. 7. Hysteresis of the sensing device for clockwise and anti-clockwiserotation.

H(s) =8.09

0.004s2 + 0.11s + 1(1)

Figure 8 reveals obviously the adequacy between the mod-eled and the measured time response behavior of the hapticdevice. Both measured and modeled frequential responses ofthe sensing device are presented in figure 9 by means of thebode diagram. The fitted model simulate appropriately thefrequential behavior of the haptic device.

1.6 1.8 2 2.2 2.4 2.6 2.80

1

2

3

4

5

6

7

8

9

10

Time (s)

Sp

eed

Ω (

rd/s

)

Experimental data

Model

Fig. 8. Step response of the SISO model.

C. Non-linear Adaptative Spring (NAS) for elastic and elastichysteresis sensing

Since the mechanical response of soft elastic mate-rial (load/deformation) does not obey to linear relationship(Hooke’s law), they can be modeled as a non-linear spring.A typical load-elongation diagram for soft tissue is shownin figure 10. We can note that loading and unloading occuron different load-deformation paths. As this diagram canbe segmented to linear areas, the mechanical behavior canbe modeled as n serial linear springs with spring constantsK1, K2, ..., Kn.

60

40

20

0

20

40

Ma

gn

itu

de

(d

B)

10 1

100

101

102

103

180

135

90

45

0

Ph

ase

(d

eg

)

Pulsation (rd/s)

Fig. 9. Bode diagram of the SISO model.

Force

Deformations h1 h2 h3

F3

F2

K1

K2

K3

F1

Fn

Es3

F’3

F’2

h’3

E’s3

K’3

K’2

δ δδ δ

Fig. 10. A typical load-elongation diagram for soft tissue.

During the load path, the strain energy Esi stored by eachlinear spring is expressed as the area below the curve andcalculated as

For i=1Es1 = E1 =

12K1δh

21 (2)

Where δh1 is the deformation resulting for the applied varia-tion load δF1

For i=2Es2 =

12K2δh

22 + δh2F1 (3)

For i=3Es3 =

12K3δh

23 + δh3F2 (4)

For i=nEsn =

12Knδh2

n + δhnFn−1 (5)

Then, the total strain energy ETi stored by the non-linearspring for a given deformation δhi is the sum of energiesstored by each linear springs as

For i=1ETi = Es1 =

12K1δh

21 (6)

NAS

α

Angular position θ

Master Slave

Homothetic gain

Micropositioning system

Load β

Homothetic gain

Derivative block

Non-linear elastic force

sensing

Operator Biological

environment

Fig. 11. Overview of the Master/Slave bilateral coupling scheme.

For i=2

ET2 = Es2 + Es1 =12K1δh

21 +

12K2δh

22 + δh2F1 (7)

For i=3

ET3 = Es3 + Es2 + Es1 =12K1δh

21 +

12δh2(K2δh2 + 2F1) +

12δh3(K3δh3 + 2F2) (8)

For i=n

ETn =12K1δh

21 +

12

n∑2

(δhi(Kiδhi + 2Fi−1)) (9)

As energy formulas are discretized, softwareimplementation becomes easier. Strain energy equationsand their iterative calculations are implemented in theslave computer based on Matlab R© Simulink Toolbox.Figure 11 shows the overview of the adopted Master/Slavebilateral coupling scheme. The homothetic gains α andβ are determined during the calibration process. Theappropriate values of the homothetic gains in our case areα = 5 10−4 µm/rd and β = 1500 N/J .

For the unload path the same approach is adopted. If we noteK

′i and δh

′i the ith constant spring and the sample deformation,

thus, the total strain energy E′Ti is expressed as

E′Tn =

12K

′1δh

′21 +

12

n∑2

(δh

′i(K

′iδh

′i + 2F

′i−1)

)(10)

IV. EXPERIMENTATIONS

Haptic sensing experimentations are conducted on humantumoral Epithilial Hella cell (EpH). The cells are chosensince they are adherent and present an interesting soft elasticbehavior. The EpH cells can be assimilated morphologicallyto elliptical cells with a thin surrounding biomembrane. Inthe present study, the average dimensions of the biologicalsample is 10 µm long, 9 µm large and 6 µm height (cf. figure12).The Epithelial Hela cells (EpH) are prepared on Petridishes with specific culture medium formed by Dulbecco’sModified Eagle’s Medium (DMEM) with high glucose and L-glutamine components and 10 % of foetal bovine serum.

Fig. 12. (A) Magnified image of the cervix Epithelial Hela cells obtained withan 63x objective. (B) The cervix Epithelial Hela cells morphology observedby fluorescence techniques.

0 5 10 15 200

5

10

15

Time (s)

Sam

ple

disp

lace

men

t (µm

)

0 5 10 15 20−5

0

5

10

Time (s)

h ’ (µ

m/s

)

0 5 10 150

1

2

3

4

5

Sample displacement (µm)

Load

(µN

)

0 5 10 15 20

−0.5

0

0.5

Time (s)

Tang

entia

l for

ce (N

)

(A) (B)

(C) (D)

Fig. 13. (A) Biological sample displacement carried out by a human operatorinterface. (B) Derivative form of the sample deformation as function of timeexperiment. (C) Elastic behavior of the EpH cells. (D) Tangential forcessensed by the human operator.

Figure 13(A) shows the biological sample displacementcarried out by a human operator using the haptic device.Displacements less than 15 µm are achieved during this ex-periment. The cell deformation δh is monitored by calculatingthe difference between the vertical position of the sample andthe cantilever deflection. Figure 13(B) shows the derivativeform of the sample deformation

.

h as function of time experi-ment. According to this figure, the studied biological sampleexhibits the same deformation amplitude whatever the load-deformation path (load and unload). Figure 13(C) reveals theelastic behavior of the biological sample as well as the elastichysteresis. This curve is obtained using the discretized strainenergy formulas presented in the last section. In oppositionto the sample deformation diagram (cf. figure 13(B)), thisfigure emphasize the difference between the load and unloadpaths. Since the elastic behavior of the biological sample isdisymmetric, the operator senses different amplitude forces forthe load and unload paths. Hence, the forces sensed are moreimportant in the case of the unload path since the gradient ofthe stored strain energy is bigger.

V. CONCLUSION

This paper has presented the development of a microforcesensing system for in vitro mechanical cell characterization.The experimental setup combines Scanning Probe Microscopy(SPM) techniques with advanced robotics approaches. Me-chanical characterization is conducted using the FSBM ontumoral human Epithelial Hela adherent cells. These exper-iments demonstrate the efficiency of the experimental setupdeveloped to explore the non-linear elastic properties of adher-ent biological samples. Non-linear elasticity theory formalismis used in order to achieve realistic elastic rendering for themacroscale.

REFERENCES

[1] D.-E. Ingber, ”Cancer as a disease of epithelial-mesenchymal interactionsand extracellular matrix regulation”.Differentiation, vol. 70, pp. 547-560,2002.

[2] C.-S. Chen, M. Mrksich, S. Huang, G.-M. Whitesides, D.-E. Ingber,”Geometric control of cell life and death”. Science, vol. 276, pp. 1425-1428, 1997.

[3] C.-M. Lo, H.-B, Wang, M.Dembo, Y.-L. Wang, ”Cell movement is guidedby the rigidity of the substrate”, Biophys J., vol. 79, pp. 1957-1964, 2000.

[4] Y. Sun and B.-J. Nelson, ”MEMS for cellular force measurements andmolecular detection”, Journal of Information Acquisition, vol. 1, no. 1,pp. 23-32, January 2004.

[5] K.-J. Van Vliet, G. Bao and S. Suresh, ”The biomechanics toolbox: ex-perimental approaches for living cells and biomolecules”, Acta MaterialiaJournal, vol. 51, pp. 5881-5905, August 2003.

[6] D.-H. Kim, S. Yun and B. Kim, ”Mechanical force response of singleliving cells using a microrobotic system”, in proceedings of the Int.Conference on Robotics and Automation, pp. 5013-5018, 2004.

[7] J. Guck, R. Ananthakrishnan, C.-C. Cunningham and J. Kas, ”Stretchingbiological cells with light”, J.Physics:Condens. Matter, vol. 14, pp. 4843-4856, May 2002.

[8] J.-M. Sharp, A.-R. Clapp and R.-B. Dickinson, ”Measurement of long-range forces on a single yeast cell using a gradient optical trap andevanescent wave light scattering”, Colloids and Surface B:Biointerfaces,vol. 27, pp. 355-364, 2003.

[9] D.-G. Grier, ”A revolution in optical manipulation”, Nature, vol. 424, pp.810-816, 2003.

[10] M. Lukkari and P. Kallio, ”Multi-purpose impedance-based measure-ment system to automate microinjection of adherent cells”, in proceedingsof the Int. Sympos. on Computational Intelligence in Robotics andAutomation”, pp. 20-26, 2005.

[11] M. Radmacher, ”Measuring the elastic properties of biological sampleswith AFM”, IEEE Engineering in Medicine and Biology, pp. 47-57, 1997.

[12] O. Sahin, G. Yaralioglu, R. Grow, S. -F. Zappe, A. Atalar, C. Quateand O. Solgaard, ”High-resolution imaging of elastic properties usingharmonic cantilevers”, Sensors and Actuators A, vol. 114, pp. 183-190,February 2004.

[13] S. Park, K. Costa and G. Ateshian, ”Microscale frictional responseof bovine articular cartilage from atomic force microscopy”, Journal ofBiomechanics, vol. 37, 1687-1697, February 2004.

[14] E.-K. Dimitriadis, F. Horkay, J. Maresca, B. Kachar and R.-S. Chadwick,”Determination of elastic moduli of thin layers of soft material using theatomic force microscope”, Biophysical Journal, vol. 82, pp. 2798-2810,May 2002.

[15] X. Yao, J. Walter, S. Burke, S. Stewart, M.-h. Jericho, D. Pink, R.Hunter and T.-J. Beveridge, ”Atomic force microscopy and theoreticalconsiderations of surface properties and turgor pressures of bacteria”,Colloids and Surfaces B: Biointerfaces, vol. 23, pp. 213-230, May 2002.

[16] M. Boukallel, M. Girot, S. Regnier, ”Enhanced near field force probingfor mechanical cell characterization”, in proceedings of the IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomecha-tronics (BioRob), February 2006.